Space Research Institute is located in the south-west region of Moscow. The best way to get to IKI is to take a metro.
You should get off at "Kalyzhskaya" metro station using the southern exit. After leaving a station lobby through glass doors you should go straight to the end of the tunnel, then take right and use the stairs to get to the surface. From this point you should follow the arrow on this map: (click image to enlarge)
Space Research Institute on Google Maps: